College

Find the products in simplest form.

1. [tex]\frac{8}{21} \cdot \frac{5}{16} =[/tex]

2. [tex]\frac{12}{25} \cdot \frac{15}{16} =[/tex]

Answer :

Sure, let's find the products of the fractions in their simplest form.

1. First Product:

Consider the fractions [tex]\(\frac{8}{21}\)[/tex] and [tex]\(\frac{5}{16}\)[/tex].

- Multiply the numerators:
[tex]\[
8 \times 5 = 40
\][/tex]

- Multiply the denominators:
[tex]\[
21 \times 16 = 336
\][/tex]

- This gives us the fraction:
[tex]\[
\frac{40}{336}
\][/tex]

- Simplify the fraction:

Find the greatest common divisor (GCD) of 40 and 336, which is 8.

- Divide the numerator and the denominator by their GCD:
[tex]\[
\frac{40 \div 8}{336 \div 8} = \frac{5}{42}
\][/tex]

So, the first product in simplest form is [tex]\(\frac{5}{42}\)[/tex].

2. Second Product:

Consider the fractions [tex]\(\frac{12}{25}\)[/tex] and [tex]\(\frac{15}{16}\)[/tex].

- Multiply the numerators:
[tex]\[
12 \times 15 = 180
\][/tex]

- Multiply the denominators:
[tex]\[
25 \times 16 = 400
\][/tex]

- This gives us the fraction:
[tex]\[
\frac{180}{400}
\][/tex]

- Simplify the fraction:

Find the greatest common divisor (GCD) of 180 and 400, which is 20.

- Divide the numerator and the denominator by their GCD:
[tex]\[
\frac{180 \div 20}{400 \div 20} = \frac{9}{20}
\][/tex]

Thus, the second product in simplest form is [tex]\(\frac{9}{20}\)[/tex].

In summary, the products are:
- [tex]\(\frac{8}{21} \cdot \frac{5}{16} = \frac{5}{42}\)[/tex]
- [tex]\(\frac{12}{25} \cdot \frac{15}{16} = \frac{9}{20}\)[/tex]